log-likelihood for the Poisson distribution

Usage

llikPois(x, lambda, full = FALSE)

Arguments

x: non negative integers
lambda: non-negative means
full: Add the data frame showing x, mean, sd as well as the fx and derivatives

Value

data frame with fx for the pdf value of with dLambda that has the derivatives with respect to the parameters at the observation time-point

Details

In an rxode2() model, you can use llikPois() but you have to use all arguments. You can also get the derivatives with llikPoisDlambda()

Author

Matthew L. Fidler

Examples

# \donttest{
llikPois(0:7, lambda = 1)
#>          fx dLambda
#> 1 -1.000000      -1
#> 2 -1.000000       0
#> 3 -1.693147       1
#> 4 -2.791759       2
#> 5 -4.178054       3
#> 6 -5.787492       4
#> 7 -7.579251       5
#> 8 -9.525161       6

llikPois(0:7, lambda = 4, full=TRUE)
#>   x lambda        fx dLambda
#> 1 0      4 -4.000000   -1.00
#> 2 1      4 -2.613706   -0.75
#> 3 2      4 -1.920558   -0.50
#> 4 3      4 -1.632876   -0.25
#> 5 4      4 -1.632876    0.00
#> 6 5      4 -1.856020    0.25
#> 7 6      4 -2.261485    0.50
#> 8 7      4 -2.821101    0.75

# In rxode2 you can use:

et <- et(0:10)
et$lambda <- 0.5

model <- function() {
  model({
    fx <- llikPois(time, lambda)
    dLambda <- llikPoisDlambda(time, lambda)
  })
}

rxSolve(model, et)
#>  
#>  
#> ℹ parameter labels from comments are typically ignored in non-interactive mode
#> ℹ Need to run with the source intact to parse comments
#>  
#>  
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> ── Solved rxode2 object ──
#> ── Parameters (value$params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions (value$inits): ──
#> named numeric(0)
#> ── First part of data (object): ──
#> # A tibble: 11 × 4
#>    time    fx dLambda lambda
#>   <dbl> <dbl>   <dbl>  <dbl>
#> 1     0 -0.5       -1    0.5
#> 2     1 -1.19       1    0.5
#> 3     2 -2.58       3    0.5
#> 4     3 -4.37       5    0.5
#> 5     4 -6.45       7    0.5
#> 6     5 -8.75       9    0.5
#> # ℹ 5 more rows
# }